I assume this is a token based survey.
The issue I see with 3 different URLs is that they might fill in the survey on 3 different days. So let's assume the first fill the "today" survey. Everything fine, you just write todays date into a question to save it.
Now they do something else and come back to the "yesterday" survey the next day. Meaning that suddenly "today" and "yesterday" is the same day.
I personally probably wouldn't use the datepicker at all and just write the actual date into a hidden equation question. You can then use this to make any calculation about yesterday, tomorrow, in 10 days, 50 days ago, whatever you want. And you can also display it.
In a token based questionnaire I would add a custom attribute and add "today", "yesterday", and "the day before" into it, so you know which questionnaire is which. You can access these token attributes from within the surveh with something like {TOKEN:ATTRIBUTE_1} and show that this questionnaire refers to "yesterday" for example. With the current date in your hidden equation question, you can calculate yesterdays date by substracting 1 day, and so on.
Of course, this doesn't solve the issue that I described in the beginning. So if the survey isn't too long, I would just create 3 question groups, one for today, yesterday and the day before and check if they respondent on the same day.
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Note: I answer at this forum in my spare time, I'm not a LimeSurvey GmbH employee.